Should I believe this Yahoo Chat?

The seriousness of it depends a great deal on the culture people are from. For example, there are several countries where incest is not punished as a crime, if the participants are adults and consenting, as you described.

I doubt that a yahoo chat could be used as evidence, as there is no proof that what they typed was actually happening. It could just have been a fantasy or role playing, something that happens quite often in chat rooms. At any rate, simply typing about it is not against the law here, that would violate freedom of speech protections in the constitution.

Furthermore, if the conversation did not go to a private IM, it is less likely that it was real, as Yahoo can and occasionally does record things going on in chats, so people do not normally have the expectation that what they say there is private. What Yahoo is mostly interested in is keeping Yahoo out of trouble, so they try to regulate behavior of people in chat rooms to prevent things like luring, or other stuff they could be blamed for not preventing. But they could not be blamed for incest happening in some-body's house.

Adult consensual incest does not harm others, and is nearly impossible to prosecute anyway, so even though it can be against the law, authorities often decline to indict without hard evidence. Making a big deal out of that chat would probably only wind up being a lot more trouble than it was worth, and would serve no good purpose.